Difference between revisions of "031 Review Part 3, Problem 8"
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<span class="exam">Give an example of a <math style="vertical-align: 0px">3\times 3</math> matrix <math style="vertical-align: 0px">A</math> with eigenvalues 5,-1 and 3. | <span class="exam">Give an example of a <math style="vertical-align: 0px">3\times 3</math> matrix <math style="vertical-align: 0px">A</math> with eigenvalues 5,-1 and 3. | ||
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\end{array}\right].</math> | \end{array}\right].</math> | ||
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| − | [[031_Review_Part_3|'''<u>Return to | + | [[031_Review_Part_3|'''<u>Return to Review Problems</u>''']] |
Latest revision as of 13:06, 15 October 2017
Give an example of a matrix Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} with eigenvalues 5,-1 and 3.
| Foundations: |
|---|
| The eigenvalues of a diagonal matrix are the entries on the diagonal. |
Solution:
| One example of such a matrix is |
|
| Since is a diagonal matrix, the eigenvalues of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} are the entries on the diagonal. |
| Hence, the eigenvalues of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} are Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 5,-1,3.} |
| Final Answer: |
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| One example is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A=\left[\begin{array}{ccc} 5 & 0 & 0\\ 0 & -1 & 0\\ 0 & 0 & 3 \end{array}\right].} |